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Rationalization and identification of binary games with correlated types

Nianqing Liu, Quang Vuong and Haiqing Xu ()

Journal of Econometrics, 2017, vol. 201, issue 2, 249-268

Abstract: This paper studies the rationalization and identification of binary games where players have correlated private types. Allowing for type correlation is crucial in global games and in models with social interactions as it represents correlated private information and homophily, respectively. Our approach is fully nonparametric in the joint distribution of types and the strategic effects in the payoffs. First, under monotone pure Bayesian Nash Equilibrium strategy, we characterize all the restrictions if any on the distribution of players’ choices imposed by the game-theoretic model as well as restrictions associated with two assumptions frequently made in the empirical analysis of discrete games. Namely, we consider exogeneity of payoff shifters relative to private information, and mutual independence of private information given payoff shifters. Second, we study the nonparametric identification of the payoff functions and types distribution. We show that the model with exogenous payoff shifters is fully identified up to a single location-scale normalization under some exclusion restrictions and rank conditions. Third, we discuss partial identification under weaker conditions and multiple equilibria. Lastly, we briefly point out the implications of our results for model testing and estimation.

Keywords: Rationalization; Identification; Discrete game; Social interactions; Global games (search for similar items in EconPapers)
JEL-codes: C14 C18 C31 C35 C52 Z13 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1016/j.jeconom.2017.08.007

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Journal of Econometrics is currently edited by T. Amemiya, A. R. Gallant, J. F. Geweke, C. Hsiao and P. M. Robinson

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